Chapter 3
Quadratic Equations, Functions,
Inequalities, and Imaginary
Numbers
Solving Equations and Inequalities with Absolute Value
One important thing to note: When you take the absolute value of an expression, then you apply
the positive and negative r

Chapter 3
Quadratic Equations, Functions,
Inequalities, and Imaginary
Numbers
Quadratic Functions and Equations
3.0.1
A Quadratic Equation
A quadratic equation is a normal everyday equation that can be written in the form
ax2 + bx + c = 0 where a 6= 0
als

Chapter 3
Quadratic Equations, Functions,
Inequalities, and Imaginary
Numbers
Analyzing Graphs of Quadratic Equations
The graph of a quadratic function is called a Parabola. The graph of every parabola evolves from the
graph of the squaring function, f (x

Chapter 3
Quadratic Equations, Functions,
Inequalities, and Imaginary
Numbers
The Complex Number System
Some functions have zeros that are not real numbers. In order to find the zeros of such functions, we
must consider the complex number system.
A little

Math 1105: College Algebra Online
Research Topics Chapter 3
Pick the topic that you like and write at least a page explaining your answer. On your essay, be sure
to specify which topic you choose and Cite your sources
1. History: Why do we have complex nu

Works Cited & internet info
Why do we have complex numbers? Why do we use i to represent a complex number? Investigate this
history behind the complex number system and perhaps any interesting facts and applications to this
system of numbers.
History of C

Chapter 1
Graphs, Functions, and Models
Linear Inequalities
An Inequality is a sentence with <, >, , as a verb. With equations, we found only 1, 2, or perhaps
3 solutions to a problem. However, Inequalities mostly deal with an infinite amount of solutions

Chapter 1
Graphs, Functions, and Models
Systems of Equations in 2 Variables
Definition 1. A System of Equations:
This is composed of two or more equations considered simultaneously.
Example 2.
xy
=
5
2x + y
=
1
The above is a system of to linear equations

Chapter 1
Graphs, Functions, and Models
Functions and Graphs
What exactly is a function? The ordered pairs from Sec. 1.1 have an x coordinate, and a y-coordinate.
Meaning, there is a correspondence between the two points.
Definition 1. Domain:
The domain,

Chapter 1
Graphs, Functions, and Models
Linear Equations, Functions, Zeros, and Applications
An Equation is a statement when two expressions are equivalent to one another. To Solve an equation
in one variable, we find all values of that variable that make

Chapter 1
Graphs, Functions, and Models
Linear Functions and Slope
The most frequently used Mathematical models, and perhaps the easiest one, is a Linear Model. Since
linear equations do not have exponents, fractions, or roots, that means they are straigh

Chapter 1
Graphs, Functions, and Models
1.1
Introduction to Graphing
Graphs
Definition 1. Graphs: A means of displaying, interpreting, and analyzing data in a visual format.
Composed of an x-axis-(Horizontal) and a y-axis-(Vertical).
The Technical term fo

Chapter 1
Graphs, Functions, and Models
Equations of Lines and Modeling
Remember from 1.3, we defined a linear function which is in turn, the slope intercept form. If we know
the slope and the y-intercept of a line, then we can find an equation of the lin

Chapter 5
Exponential and Logarithmic
Functions
Logarithmic Functions
Remember back in Section 5.1 when I told you that everything (Generally Speaking) has an Inverse?
Well weve been dealing with exponential functions so a question you may have is. Whats

Chapter 5
Exponential and Logarithmic
Functions
Inverse Functions
Remember the one guy that had an apple fall on his head? Yeah, he came up with 3 important laws
in physics. One of those laws is the following: For every action, there is an opposite reacti

Chapter 5
Exponential and Logarithmic
Functions
Exponential Functions
We saved the best chapter for last. This chapter, dealing with exponential and logarithmic functions is
perhaps the most applied part of any college algebra course. Anytime you turn on

Chapter 5
Exponential and Logarithmic
Functions
Solving Exponential and Logarithmic Equations
In this section, youll learn how to solve equations with unknowns in the exponent parts.
5.0.1
The Base-Exponent Property
For any number, a > 0, and as long as a